exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 13.4s

Alternatives: 4

Speedup: N/A×

• could not determine a ground truth

  1. w = 2.00000000000000007e154
  2. l = -2

Specification

Math

\[\begin{array}{l} \\ e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = exp(-w) * (l ** exp(w))
end function

Java

public static double code(double w, double l) {
	return Math.exp(-w) * Math.pow(l, Math.exp(w));
}

Python

def code(w, l):
	return math.exp(-w) * math.pow(l, math.exp(w))

Julia

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end

MATLAB

function tmp = code(w, l)
	tmp = exp(-w) * (l ^ exp(w));
end

Wolfram

code[w_, l_] := N[(N[Exp[(-w)], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = exp(-w) * (l ** exp(w))
end function

Java

public static double code(double w, double l) {
	return Math.exp(-w) * Math.pow(l, Math.exp(w));
}

Python

def code(w, l):
	return math.exp(-w) * math.pow(l, math.exp(w))

Julia

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end

MATLAB

function tmp = code(w, l)
	tmp = exp(-w) * (l ^ exp(w));
end

Wolfram

code[w_, l_] := N[(N[Exp[(-w)], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{e}^{\left(w + 1\right)}}{e}} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (/ (pow l (exp w)) (/ (pow E (+ w 1.0)) E)))

C

double code(double w, double l) {
	return pow(l, exp(w)) / (pow(((double) M_E), (w + 1.0)) / ((double) M_E));
}

Java

public static double code(double w, double l) {
	return Math.pow(l, Math.exp(w)) / (Math.pow(Math.E, (w + 1.0)) / Math.E);
}

Python

def code(w, l):
	return math.pow(l, math.exp(w)) / (math.pow(math.e, (w + 1.0)) / math.e)

Julia

function code(w, l)
	return Float64((l ^ exp(w)) / Float64((exp(1) ^ Float64(w + 1.0)) / exp(1)))
end

MATLAB

function tmp = code(w, l)
	tmp = (l ^ exp(w)) / ((2.71828182845904523536 ^ (w + 1.0)) / 2.71828182845904523536);
end

Wolfram

code[w_, l_] := N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] / N[(N[Power[E, N[(w + 1.0), $MachinePrecision]], $MachinePrecision] / E), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.7%

      \[\leadsto \color{blue}{\frac{1}{e^{w}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   2. remove-double-neg 99.7%

      \[\leadsto \frac{1}{e^{\color{blue}{-\left(-w\right)}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   3. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{1 \cdot {\ell}^{\left(e^{w}\right)}}{e^{-\left(-w\right)}}} \]

   4. *-lft-identity 99.7%

      \[\leadsto \frac{\color{blue}{{\ell}^{\left(e^{w}\right)}}}{e^{-\left(-w\right)}} \]

   5. remove-double-neg 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{\color{blue}{w}}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-un-lft-identity 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{\color{blue}{1 \cdot w}}} \]

   2. exp-prod 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{{\left(e^{1}\right)}^{w}}} \]

   3. expm1-log1p-u 77.1%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{{\left(e^{1}\right)}^{\color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(w\right)\right)\right)}}} \]

   4. expm1-undefine 77.1%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{{\left(e^{1}\right)}^{\color{blue}{\left(e^{\mathsf{log1p}\left(w\right)} - 1\right)}}} \]

   5. pow-sub 77.1%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{\frac{{\left(e^{1}\right)}^{\left(e^{\mathsf{log1p}\left(w\right)}\right)}}{{\left(e^{1}\right)}^{1}}}} \]

   6. exp-1-e 77.1%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{\color{blue}{e}}^{\left(e^{\mathsf{log1p}\left(w\right)}\right)}}{{\left(e^{1}\right)}^{1}}} \]

   7. log1p-undefine 77.1%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{e}^{\left(e^{\color{blue}{\log \left(1 + w\right)}}\right)}}{{\left(e^{1}\right)}^{1}}} \]

   8. rem-exp-log 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{e}^{\color{blue}{\left(1 + w\right)}}}{{\left(e^{1}\right)}^{1}}} \]

   9. pow1 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{e}^{\left(1 + w\right)}}{\color{blue}{e^{1}}}} \]

   10. exp-1-e 99.7%

       \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{e}^{\left(1 + w\right)}}{\color{blue}{e}}} \]

6. Applied egg-rr 99.7%

   \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{\frac{{e}^{\left(1 + w\right)}}{e}}} \]
7. Step-by-step derivation

   1. +-commutative 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\frac{{e}^{\color{blue}{\left(w + 1\right)}}}{e}} \]

8. Simplified 99.7%

   \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{\frac{{e}^{\left(w + 1\right)}}{e}}} \]
9. Add Preprocessing

Alternative 2: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (/ (pow l (exp w)) (exp w)))

C

double code(double w, double l) {
	return pow(l, exp(w)) / exp(w);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = (l ** exp(w)) / exp(w)
end function

Java

public static double code(double w, double l) {
	return Math.pow(l, Math.exp(w)) / Math.exp(w);
}

Python

def code(w, l):
	return math.pow(l, math.exp(w)) / math.exp(w)

Julia

function code(w, l)
	return Float64((l ^ exp(w)) / exp(w))
end

MATLAB

function tmp = code(w, l)
	tmp = (l ^ exp(w)) / exp(w);
end

Wolfram

code[w_, l_] := N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] / N[Exp[w], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.7%

      \[\leadsto \color{blue}{\frac{1}{e^{w}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   2. remove-double-neg 99.7%

      \[\leadsto \frac{1}{e^{\color{blue}{-\left(-w\right)}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   3. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{1 \cdot {\ell}^{\left(e^{w}\right)}}{e^{-\left(-w\right)}}} \]

   4. *-lft-identity 99.7%

      \[\leadsto \frac{\color{blue}{{\ell}^{\left(e^{w}\right)}}}{e^{-\left(-w\right)}} \]

   5. remove-double-neg 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{\color{blue}{w}}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 97.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \frac{\ell}{e^{w}} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (/ l (exp w)))

C

double code(double w, double l) {
	return l / exp(w);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l / exp(w)
end function

Java

public static double code(double w, double l) {
	return l / Math.exp(w);
}

Python

def code(w, l):
	return l / math.exp(w)

Julia

function code(w, l)
	return Float64(l / exp(w))
end

MATLAB

function tmp = code(w, l)
	tmp = l / exp(w);
end

Wolfram

code[w_, l_] := N[(l / N[Exp[w], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.7%

      \[\leadsto \color{blue}{\frac{1}{e^{w}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   2. remove-double-neg 99.7%

      \[\leadsto \frac{1}{e^{\color{blue}{-\left(-w\right)}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   3. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{1 \cdot {\ell}^{\left(e^{w}\right)}}{e^{-\left(-w\right)}}} \]

   4. *-lft-identity 99.7%

      \[\leadsto \frac{\color{blue}{{\ell}^{\left(e^{w}\right)}}}{e^{-\left(-w\right)}} \]

   5. remove-double-neg 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{\color{blue}{w}}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 99.2%

   \[\leadsto \frac{\color{blue}{\ell}}{e^{w}} \]
6. Add Preprocessing

Alternative 4: 45.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ e^{-w} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (exp (- w)))

C

double code(double w, double l) {
	return exp(-w);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = exp(-w)
end function

Java

public static double code(double w, double l) {
	return Math.exp(-w);
}

Python

def code(w, l):
	return math.exp(-w)

Julia

function code(w, l)
	return exp(Float64(-w))
end

MATLAB

function tmp = code(w, l)
	tmp = exp(-w);
end

Wolfram

code[w_, l_] := N[Exp[(-w)], $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
2. Step-by-step derivation

   1. exp-neg 99.7%

      \[\leadsto \color{blue}{\frac{1}{e^{w}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   2. remove-double-neg 99.7%

      \[\leadsto \frac{1}{e^{\color{blue}{-\left(-w\right)}}} \cdot {\ell}^{\left(e^{w}\right)} \]

   3. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{1 \cdot {\ell}^{\left(e^{w}\right)}}{e^{-\left(-w\right)}}} \]

   4. *-lft-identity 99.7%

      \[\leadsto \frac{\color{blue}{{\ell}^{\left(e^{w}\right)}}}{e^{-\left(-w\right)}} \]

   5. remove-double-neg 99.7%

      \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{e^{\color{blue}{w}}} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add-cbrt-cube 61.0%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right) \cdot \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}} \]

   2. pow1/3 59.7%

      \[\leadsto \color{blue}{{\left(\left(\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right) \cdot \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right)}^{0.3333333333333333}} \]

   3. pow-to-exp 59.8%

      \[\leadsto \color{blue}{e^{\log \left(\left(\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right) \cdot \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right) \cdot 0.3333333333333333}} \]

   4. pow3 59.8%

      \[\leadsto e^{\log \color{blue}{\left({\left(\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right)}^{3}\right)} \cdot 0.3333333333333333} \]

   5. log-pow 93.8%

      \[\leadsto e^{\color{blue}{\left(3 \cdot \log \left(\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}\right)\right)} \cdot 0.3333333333333333} \]

   6. log-div 93.8%

      \[\leadsto e^{\left(3 \cdot \color{blue}{\left(\log \left({\ell}^{\left(e^{w}\right)}\right) - \log \left(e^{w}\right)\right)}\right) \cdot 0.3333333333333333} \]

   7. log-pow 93.8%

      \[\leadsto e^{\left(3 \cdot \left(\color{blue}{e^{w} \cdot \log \ell} - \log \left(e^{w}\right)\right)\right) \cdot 0.3333333333333333} \]

   8. add-log-exp 93.8%

      \[\leadsto e^{\left(3 \cdot \left(e^{w} \cdot \log \ell - \color{blue}{w}\right)\right) \cdot 0.3333333333333333} \]

   9. fma-neg 93.8%

      \[\leadsto e^{\left(3 \cdot \color{blue}{\mathsf{fma}\left(e^{w}, \log \ell, -w\right)}\right) \cdot 0.3333333333333333} \]

6. Applied egg-rr 93.8%

   \[\leadsto \color{blue}{e^{\left(3 \cdot \mathsf{fma}\left(e^{w}, \log \ell, -w\right)\right) \cdot 0.3333333333333333}} \]

7. Taylor expanded in w around inf 43.0%

   \[\leadsto e^{\color{blue}{-1 \cdot w}} \]
8. Step-by-step derivation

   1. mul-1-neg 43.0%

      \[\leadsto e^{\color{blue}{-w}} \]

9. Simplified 43.0%

   \[\leadsto e^{\color{blue}{-w}} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))